E36 alarm going off same time every day - Please help?

I recently aquired a 1993 E36 and the alarm was tripping at 5.30 every morning. It has the BMW alarm system with the single button remote. I couldn't find why it was doing this and I disconnected the battery for a couple of minutes to try that, but it went off exactly 12 hours after I connected the battery again. So now if I disconnect the battery and reconect the battery, the alarm goes off 12 hours later (to the minute) and then every 24 hours after that at exactly the same time ~ Please help, its driving me mad.

George
November 2009